State Standards: GLEs/GSEs National Content Standards:
Grade Span Expectations [Math]:
M(N&O)–10–8 Applies properties of numbers to solve problems, to simplify computations, or to compare and contrast the properties of numbers and number systems. M(F&A)–10–1 Identifies, extends, and generalizes a variety of patterns (linear and nonlinear) represented by models, tables, sequences, or graphs to solve problems. M(PRP)–HS–1 Students will use problem-solving strategies to investigate and understand increasingly complex mathematical content and be able to:
• Expand the repertoire of problem-solving strategies and use those strategies in more sophisticated ways.
• Use technology whenever appropriate to solve real-world problems (e.g., personal finance, wages, banking and credit, home improvement problems, measurement, taxes, business situations, purchasing, and transportation).
• Formulate and redefine problem situations as needed to arrive at appropriate conclusions.
Grade Span Expectations [Physics]:
PS3 (7-8) 8: Students demonstrate and understanding of motion by… (8a)… measuring the distance and time for a given moving object and using those values to calculate speed. (8b)… Solving for any unknown in the expression v=d/t given values for the other two variables. (8c)… Differentiating between speed, velocity and acceleration.
PS3 (9-11) 8: Students demonstrate and understanding of forces and motion by… (8a)… Predicting and/or graphing the path of an object in different reference planes and explain how and why it occurs. (8b)… Using modeling, illustrating, and graphing to explain how distance and velocity change over time for a free falling object.
PS3 (Ext) 8: Students demonstrate an understanding of forces and motion by… (8aa)… Using a quantitative representation of how distance and velocity change over time for a free falling object.
Context of the Lesson Where does this lesson fit in the curriculum and instructional context? Is it the opening of a unit or a series of lessons?
This lesson was designed to fit in to the beginning of a two-dimensional kinematics unit. Students should have already been exposed to the concepts of distance, velocity, and acceleration and they should be familiar with solving problems related to these concepts. They will have recently finished a One-Dimensional kinematics unit and will be familiar with the 3 major kinematics equations for 1 dimension. Students should have also been exposed to the concept of gravity and should be familiar with working with problems that involve objects in free fall. They should be able to solve problems involving objects moving horizontally and objects moving vertically.
The projectile motion units puts all of these concepts together and students will learn how to solve problems involving objects moving in both the x and y direction. This lesson is designed to review ALL of the important concepts that the students have already learned. No new material will be presented in this lesson. Through this lesson the teacher can gauge the readiness of the students to move on to projectile motion.
Opportunities to Learn
Differentiation: Materials, Learners and Environments
Plans to differentiate instruction:
Throughout this lesson there are several different forms of instruction. There is direct instruction, group work, and independent student work. I also incorporate videos and visual representations of problems within the lesson. In this way the lesson will accommodate for several different types of learners. The students won’t simply be sitting at their desks for the entire lesson but rather they will be working in groups and walking around the room to the different stations that I will have set up for the second activity. This will keep them engaged. The lesson will also be continuously changing to keep the students interested with what they are learning. In addition to this, throughout the lesson, I will have challenges for the advanced students. During the second activity I will create questions of varying difficulty and I will incorporate some challenging questions for the students may be more advanced than the others. These questions will be color-coded so that advanced students can seek out the more difficult problems if they want to challenge themselves. For the students that may be struggling I will offer some extra support throughout the activities. I will rotate throughout the groups and offer guiding questions and assistance to the students that seem to be struggling with the task. The second activity also incorporates very basic problems so that these students can build their self efficacy and become more confident in the subject matter and in their ability. Accommodations and modifications: During this lesson I will make accommodations and modifications for the struggling students within the class. I will allow the students to take as much time as they need on the quiz that I will give them at the beginning of the class period. Therefore students will not feel rushed and will be able to take their time on the assessment. I will also group the students randomly during the lesson so students will be given the opportunity to learn from one another and see various different points of view. Environment factors: In preparing this lesson it is important to consider how the room will be set up and where the stations will be placed around the room. The desks should be arranged as usual for the assessment that will take place during the first 20 minutes of class. Then, during the first activities students can work together in groups at the lab benches. The second activity requires there to be 15 different stations throughout the room. I will create these ahead of time and place the challenges within envelopes that will be hung at the different lab benches throughout the room. In this way the students will not be able to peek at the challenges for the second activity when they are performing the first activity. Materials: ü Envelopes ü 15 problems of varying difficulty ü Calculators ü Large chart paper
Objectives
Students will demonstrate their understanding of 1-Dimensional kinematics and objects in free fall by successfully completing 5 problems, which deal with these concepts.
#
Instructional Procedures
LAUNCH A: The class period will begin and I will hand out Quiz #1 to the students. This quiz will cover the concepts that were learned in the previous lesson (breaking vectors into components). They will be allowed to use their calculators but that is all. They will be given 25 minutes to complete the assessment. If they have still not finished the assessment I will allow them to continue working while I begin the next activity. The first part of this lesson is designed to get the students excited about what they will be learning in the coming unit. “In the past few weeks we have talked about motion in the x direction as well as motion in the y direction. We are now starting a unit of 2 dimensional motion in which we will put it all together” “Can you think of examples of things that move in both the x and y directions?” The “Daily Challenge” for the students will be to work in groups to brainstorm a list of different things (projectiles, animals, vehicles, etc) from the real world that move in the x and the y direction. Students will create a list of examples on a large piece of paper and they can include small sketches of each of the examples. We will then post these in the front of the class and discuss whether or not we are missing any examples. I will have a few videos to show them about “pumpkin chunking”. This is a yearly event in which people create devices that will throw pumpkins. This is a great example of projectile motion and is also very entertaining. This activity will hopefully get the students excited about the unit and will show them that what they will be learning can be easily applied to the real world and to their own lives. “Before we start this unit I want to make sure that we all remember the important concepts that we learned in the previous unit. To do this we are going to play a game!” In order to review the 1D dimensional kinematics unit I will randomly split all of the students into groups of 3 and we will have a small competition. EXPLORE A: Positioned around the room there will be 15 different stations each with a different challenge. The students will have to visit each station and complete the challenge. They will work in groups of 3 and will have to record all of their work as well as their answers on notebook paper that they will each have to turn in at the end of the day. The 15 different challenges can be seen on the next sheet. Each challenge has a different level of difficulty and will be color-coded as such (Black=Difficult, Blue=Intermediate, Green=Easy). The more difficult problems are worth more points while the simple problems are not weighted as heavily (Black=5pts, Blue=3pts, Black=1pt. All will be multiple parts and I will want to see the students work for each part in order for them to get credit. I will collect and grade each group’s work and the group that received the most amount of points (for correct responses) will be awarded 2 Extra Credit points each for the final unit assessment. Students can complete these challenges at their own pace and when groups finish with one they can move on to another open station. The activity will be timed and they will only have 35-40 minutes to work on the problems. After this time has passed I will collect all of the work and the students will reconvene at their desks. I will quickly tally the totals for the groups and will award the winning group their prize. If students are having trouble with the problems that I present to them I will walk around the room and offer them assistance. “What variables do we know/ what variables are given in this particular problem?” “Draw a diagram to help yourself visualize what is actually happening” “What kinematics equations can we use in this scenario to help us find the variable that we are looking for?” “Does 1 equation with two unknowns help us in any way? What other information would we need in order to solve such a problem? If we have two equations and 2 unknowns can we solve for the two unknowns?” For the students that find this activity very easy there will be more challenging problems that they can focus there attention on. This will allow them to challenge themselves by seeking out the problems that I designated as being the most challenging. SUMMARIZE/SHARE A: Once I have awarded the winning group with their prize I will ask the students if they would like to go over any of the problems that were in the activity. If there are certain problems that students struggled with I will ask if there is a group (that got the problem correct) that would like to explain the process that they used. This will allow us to review the information together and students can learn from the other groups.
Assessment
In order to assess my students during this investigation I will determine whether each student has successfully completed the objective from above. Launch A: During the Launch phase of the first activity, the student will be informally assessed and I will determine whether or not they are able to connect what they are learning within the physics classroom to their own lives and to the world outside of the walls of the classroom. By observing their ability to formulate a list of examples of projectile motion in the real world I will be able to determine if they truly understand the concepts. Explore A: During the explore phase of this lesson I will be assessing the students informally by observing the groups. I will be assessing them on their problem solving skills as well as their ability to work together in groups. I will take notes while I walk around the classroom. Summarize A: During the summarize phase of the first activity the students will have to explain their thought process as well as their results. This will give me an opportunity to further gauge their understanding of the material. If a student can fully explain what they found and how it relates to right triangles in general then I can conclude that they have a firm grasp on the necessary concepts. I can also assess the students in a formal way by determining if the results that they found are accurate.
Reflections This section to be completed only if lesson plan is implemented.
Lesson Implementation: Was not able to implement this lesson yet.
Lesson #1: 1D Kinematics Review
Lesson Title
1D Kinematics Review
National Content Standards:
M(N&O)–10–8 Applies properties of numbers to solve problems, to simplify computations, or to compare and contrast the properties of numbers and number systems.
M(F&A)–10–1 Identifies, extends, and generalizes a variety of patterns (linear and nonlinear) represented by models, tables, sequences, or graphs to solve problems.
M(PRP)–HS–1 Students will use problem-solving strategies to investigate and understand increasingly complex mathematical content and be able to:
• Expand the repertoire of problem-solving strategies and use those strategies in more sophisticated ways.
• Use technology whenever appropriate to solve real-world problems (e.g., personal finance, wages, banking and credit, home improvement problems, measurement, taxes, business situations, purchasing, and transportation).
• Formulate and redefine problem situations as needed to arrive at appropriate conclusions.
Grade Span Expectations [Physics]:
PS3 (7-8) 8: Students demonstrate and understanding of motion by…
(8a)… measuring the distance and time for a given moving object and using those values to calculate speed.
(8b)… Solving for any unknown in the expression v=d/t given values for the other two variables.
(8c)… Differentiating between speed, velocity and acceleration.
PS3 (9-11) 8: Students demonstrate and understanding of forces and motion by…
(8a)… Predicting and/or graphing the path of an object in different reference planes and explain how and why it occurs.
(8b)… Using modeling, illustrating, and graphing to explain how distance and velocity change over time for a free falling object.
PS3 (Ext) 8: Students demonstrate an understanding of forces and motion by…
(8aa)… Using a quantitative representation of how distance and velocity change over time for a free falling object.
Where does this lesson fit in the curriculum and instructional context? Is it the opening of a unit or a series of lessons?
The projectile motion units puts all of these concepts together and students will learn how to solve problems involving objects moving in both the x and y direction. This lesson is designed to review ALL of the important concepts that the students have already learned. No new material will be presented in this lesson. Through this lesson the teacher can gauge the readiness of the students to move on to projectile motion.
Differentiation: Materials, Learners and Environments
Throughout this lesson there are several different forms of instruction. There is direct instruction, group work, and independent student work. I also incorporate videos and visual representations of problems within the lesson. In this way the lesson will accommodate for several different types of learners. The students won’t simply be sitting at their desks for the entire lesson but rather they will be working in groups and walking around the room to the different stations that I will have set up for the second activity. This will keep them engaged. The lesson will also be continuously changing to keep the students interested with what they are learning.
In addition to this, throughout the lesson, I will have challenges for the advanced students. During the second activity I will create questions of varying difficulty and I will incorporate some challenging questions for the students may be more advanced than the others. These questions will be color-coded so that advanced students can seek out the more difficult problems if they want to challenge themselves.
For the students that may be struggling I will offer some extra support throughout the activities. I will rotate throughout the groups and offer guiding questions and assistance to the students that seem to be struggling with the task. The second activity also incorporates very basic problems so that these students can build their self efficacy and become more confident in the subject matter and in their ability.
Accommodations and modifications:
During this lesson I will make accommodations and modifications for the struggling students within the class. I will allow the students to take as much time as they need on the quiz that I will give them at the beginning of the class period. Therefore students will not feel rushed and will be able to take their time on the assessment. I will also group the students randomly during the lesson so students will be given the opportunity to learn from one another and see various different points of view.
Environment factors:
In preparing this lesson it is important to consider how the room will be set up and where the stations will be placed around the room. The desks should be arranged as usual for the assessment that will take place during the first 20 minutes of class. Then, during the first activities students can work together in groups at the lab benches. The second activity requires there to be 15 different stations throughout the room. I will create these ahead of time and place the challenges within envelopes that will be hung at the different lab benches throughout the room. In this way the students will not be able to peek at the challenges for the second activity when they are performing the first activity.
Materials:
ü Envelopes
ü 15 problems of varying difficulty
ü Calculators
ü Large chart paper
- Students will demonstrate their understanding of 1-Dimensional kinematics and objects in free fall by successfully completing 5 problems, which deal with these concepts.
#Instructional Procedures
The class period will begin and I will hand out Quiz #1 to the students. This quiz will cover the concepts that were learned in the previous lesson (breaking vectors into components). They will be allowed to use their calculators but that is all. They will be given 25 minutes to complete the assessment. If they have still not finished the assessment I will allow them to continue working while I begin the next activity.
The first part of this lesson is designed to get the students excited about what they will be learning in the coming unit.
“In the past few weeks we have talked about motion in the x direction as well as motion in the y direction. We are now starting a unit of 2 dimensional motion in which we will put it all together”
“Can you think of examples of things that move in both the x and y directions?”
The “Daily Challenge” for the students will be to work in groups to brainstorm a list of different things (projectiles, animals, vehicles, etc) from the real world that move in the x and the y direction. Students will create a list of examples on a large piece of paper and they can include small sketches of each of the examples. We will then post these in the front of the class and discuss whether or not we are missing any examples. I will have a few videos to show them about “pumpkin chunking”. This is a yearly event in which people create devices that will throw pumpkins. This is a great example of projectile motion and is also very entertaining. This activity will hopefully get the students excited about the unit and will show them that what they will be learning can be easily applied to the real world and to their own lives.
“Before we start this unit I want to make sure that we all remember the important concepts that we learned in the previous unit. To do this we are going to play a game!”
In order to review the 1D dimensional kinematics unit I will randomly split all of the students into groups of 3 and we will have a small competition.
EXPLORE A:
Positioned around the room there will be 15 different stations each with a different challenge. The students will have to visit each station and complete the challenge. They will work in groups of 3 and will have to record all of their work as well as their answers on notebook paper that they will each have to turn in at the end of the day.
The 15 different challenges can be seen on the next sheet. Each challenge has a different level of difficulty and will be color-coded as such (Black=Difficult, Blue=Intermediate, Green=Easy). The more difficult problems are worth more points while the simple problems are not weighted as heavily (Black=5pts, Blue=3pts, Black=1pt. All will be multiple parts and I will want to see the students work for each part in order for them to get credit. I will collect and grade each group’s work and the group that received the most amount of points (for correct responses) will be awarded 2 Extra Credit points each for the final unit assessment.
Students can complete these challenges at their own pace and when groups finish with one they can move on to another open station.
The activity will be timed and they will only have 35-40 minutes to work on the problems. After this time has passed I will collect all of the work and the students will reconvene at their desks. I will quickly tally the totals for the groups and will award the winning group their prize.
If students are having trouble with the problems that I present to them I will walk around the room and offer them assistance.
“What variables do we know/ what variables are given in this particular problem?”
“Draw a diagram to help yourself visualize what is actually happening”
“What kinematics equations can we use in this scenario to help us find the variable that we are looking for?”
“Does 1 equation with two unknowns help us in any way? What other information would we need in order to solve such a problem? If we have two equations and 2 unknowns can we solve for the two unknowns?”
For the students that find this activity very easy there will be more challenging problems that they can focus there attention on. This will allow them to challenge themselves by seeking out the problems that I designated as being the most challenging.
SUMMARIZE/SHARE A:
Once I have awarded the winning group with their prize I will ask the students if they would like to go over any of the problems that were in the activity. If there are certain problems that students struggled with I will ask if there is a group (that got the problem correct) that would like to explain the process that they used. This will allow us to review the information together and students can learn from the other groups.
Launch A:
During the Launch phase of the first activity, the student will be informally assessed and I will determine whether or not they are able to connect what they are learning within the physics classroom to their own lives and to the world outside of the walls of the classroom. By observing their ability to formulate a list of examples of projectile motion in the real world I will be able to determine if they truly understand the concepts.
Explore A:
During the explore phase of this lesson I will be assessing the students informally by observing the groups. I will be assessing them on their problem solving skills as well as their ability to work together in groups. I will take notes while I walk around the classroom.
Summarize A:
During the summarize phase of the first activity the students will have to explain their thought process as well as their results. This will give me an opportunity to further gauge their understanding of the material. If a student can fully explain what they found and how it relates to right triangles in general then I can conclude that they have a firm grasp on the necessary concepts. I can also assess the students in a formal way by determining if the results that they found are accurate.
This section to be completed only if lesson plan is implemented.